等差数列an的公差和等比数列bn的公比相等,且都等于d(d>0）d不等于0,若a1=b1,a3=5b3,a5=5b5求an,bn_数学解答

等差数列an的公差和等比数列bn的公比相等,且都等于d(d>0）d不等于0,若a1=b1,a3=5b3,a5=5b5求an,bn

人气：150 ℃　时间：2020-03-28 10:56:59

解答

设an=a1+(n-1)d,bn=b1d^(n-1)=a1d^(n-1)a3=a1+2d,b3=a1d^2a5=a1+4d,b5=a1d^4a1+2d=5a1d^2a1+4d=5a1d^4 d^2=1+(2/5)√5d=√[1+(2/5)√5]a1=2d/(5d^2-1)=2√[1+(2/5)√5]/{5[1+(2/5)√5]-1}=2√[5+2√5]/[10+4√5]=1/...